Efficient calculation method of the derivative of traveltime and amplitude using sweet algorithm for refraction tomography

Inversion of traveltime requires an efficient algorithm for computing the traveltime as well as its Fréchet derivative. We compute the traveltime of the head waves using the damped wave solution in the Laplace domain, and then present a new algorithm for calculating the Fréchet derivative of the head wave traveltimes and amplitudes by exploiting the numerical structure of the finite element method, the modern sparse matrix technology, and SWEET algorithm developed recently. Next, we use a properly regularized steepest descent method to invert the traveltime of the Marmousi-2 model. Through our numerical tests, we will demonstrate that refraction tomography with large aperture data can be used to construct the initial velocity model for the pre-stack depth migration.